The main challenge of this boss lies within a 30 second poison debuff that reduces healing by 75% (90% on 25man). Since shadow priests cannot dispel poisons, this boss becomes extremely difficult if not impossible for shadow priests. Fortunately there is a way to overcome this debuff via the use of an item called "Immature Venom Sac" which cures poisons and has no cooldown.
With the poison debuff issue solved, the rest of the fight becomes a lot more trivial. Although care must still be taken with the poison debuff since it is understood that it has no cooldown and the boss can cast it very frequently, sometimes reapplying it as soon as it is dispelled. The boss can also cause a player to become web wrapped against the wall every 40 seconds, but this is not applied to main tanks so that mechanic is also circumvented. However this does mean that care must be taken when aggro dumping onto your Shadowfiend to make sure that web wrap does not occur. Spiderling adds can also occasionally spawn under the boss, and these can be easily dealt with using Mind Sear (or Holy Nova). She also has an occasional 5 sec stun and there is not much that can be done about apart from maybe Dispersion to minimize the damage taken.
The only other issue that can cause potential problems is that the boss has a soft enrage at 30% health which increases her attack speed and damage. The best way to deal with her at this stage is to aggro dump with Shadowfiend and burn. Again care must be taken when aggro dumping to make sure web wrap does not occur.
The way to do this fight without using the Immature Venom Sac is a lot more difficult and is really dependent on luck. Since the poison debuff has no CD, the boss applies it at irregular intervals. This means that the boss can reapply it as soon as it falls off. On the other hand the boss may not reapply it for several seconds after it falls off and that is the window of opportunity to heal up and continue the fight. The rest of the strategy is similar to the above.